Faversham itself is just adorable in the daytime but on Friday/Saturday nights it gets a bit feral. Just like any town these days I guess. I have friends who live in the town itself (you can get really lovely houses at very reasonable prices) and they say it is fine but they do get woken up every now and then by drunken singing and suchlike. I would definately advise that you go walk round about 10pm on a Saturday night. It's not London of course, but it is odd, if all you've ever seen is the quaint old market place of a daytime. Canterbury, surprisingly is nowhere near as strange in this way even though it is stuffed to the gills with students.
In Faversham you want to buy either in Abbey Street or the Mall, or in the small streets near the brewerey (warning, can smell strange at times near brewery) or out on the A2 which is still fine to get to the station. Be careful of the new builds in the town - none of them are selling (at all). The 'Brents' is very popular with young families, has lots of homes that are a step up from starter homes, very attractive in design, and not too expensive.
If you had a car I would suggest Boughton, Hernhill, Sheldwich. All fabulous places, but no train links.
If you need to walk to a station but live in a village then choices are more limited. Teynham is possible but not a village I would personally want to live in - doesn't seem to have a villagey character.
Selling is a very popular place - it is one stop from Faversham and then you have to change trains (it is only about 5 minutes from Faversham) There is a big selection of housing from manor house to choc-box-cottage to ex-local authority. The school there has a very good reputation (as does Hernhill) and some of my friends saved loads by taking their boy out of private to go here, and he has thrived. Not sure if Selling has a soul though - it is spread over a wide area.
Slightly further along the line is Whitstable of course which is fab (but I guess you know that), BUT you get less for your money house-wise because it has turned a bit 'Islington-by-the-sea'
Chestfield is very boring but has good bus/train links and is very safe (in a Margo & Jerry kind of way). Your kids will hate you for living there but they'll certainly not be shooting up smack in the playing fields whilst hating you.
Canterbury is nice but you will struggle to find something you like within a reasonable walk of Canterbury East
Check out the new fast train route that is coming on-line next November - I think it might go through Wye and Chilham which then opens up some nice opportunities further afield, but still within an hour of Stratford station.
I love living round here - DP often drives up to the wharf, and I am usually on the 6.36 to London Bridge.